+113 Two hundred fence posts are to be placed into the ground in a straight line, 2m apart. The fence posts are stacked in a pile along this same line, 2m from the position of the first post to be put in. Maybell is going to put in the posts one at a time in order, and each post she puts in is farther away from the pile. Maybell can only carry one post at a time, and so she always walks back to the pile to get the next post. If Maybell starts at the pile, how many kilometers mush she walk to finish the job?
+37153 1st post she walks 2m to put the post in, then 2m back to the pile = 4m
2nd post is at the pile = 0
3rd = 4
4th = 8
5th = 12
nth one = (n-2) *4
Total distance = 4 + \(\sum_{2}^{200}\)(n-2)*4 meters (this assumes she walks back to the pile location after the final post placement)
78,808 m = 78.808 km
IF she doesn't walk back to the pile it is 396 m LESS.
+129899 Note that Maybell walks
4m total to put in the first post [ 2 out, 2 back ]
8m total to put in the second post [ 4 out, 4 back ]
12m total to put in the third post....etc. [ 6 out, 6 back ] ....etc.....
For the first 199 posts, we have
4 (1 + 2 + 3 + .....+ 199)
The sum of the first 199 positive integers can be expressed as
199 * 200 / 2 = 19900
And 4 times this is 79600 m
For the last post...she walks 2m * 200 = 400 m and doesn't need to return to the pile
So...the total distance walked is 79600m + 400m = 80000 m = 8 km
